Distributed Task Allocation for Self-Interested Agents with Partially Unknown Rewards

Nirabhra Mandal, Mohammad Khajenejad and Sonia Martínez
IEEE Transactions on Automatic Control, submitted

Abstract:

This paper provides a novel solution to a task allocation problem, by which a group of agents assigns on the assignment of a discrete set of tasks in an optimal and distributed manner. In this setting, heterogeneous agents have individual preferences and associated rewards for doing each task; however, these rewards are only known asymptotically. The assignment problem is formulated by means of a combinatorial partition game for known rewards, with no constraints on the number of tasks per agent. We relax this into a weight game, which together with the former, are shown to contain the optimal task allocation in the corresponding set of Nash Equilibria (NE). We then propose a projected, best-response, ascending gradient dynamics (\dynacr) that converges to a NE in finite time. This forms the basis of a distributed online version that can deal with a converging sequence of rewards by means of an agreement sub-routine. We present simulations that support our results.

Files: main.pdf

Bib-tex entry:

@article{NM-MK-SM:24-tac,
author = {N. Mandal and M. Khajenejad and S. Mart{\'\i}nez},
title = { Distributed Task Allocation for Self-Interested Agents with Partially Unknown Rewards},
journal= {IEEE Transactions on Automatic Control},
pages = {},
volume = {},
number = {},
year = {2024},
note={Under review}
}